Question

The number of divisors of $3\times 7^3,7\times {11}^2$ and $2\times 61$ are in:

• A. AP
• B. GP
• C. HP
• D. none of these

Answer 1

Answer: (A)

Key Idea : If $a,b$ and $c$ are the prime numbers,
then the divisors of $a^{n_1}{b}^{n_2}{c}^{n_3}$ is
$\left(n_1+1\right)\left(n_2+1\right)\left(n_3+1\right)$
The number of divisors of $3\times 7^3=8$,
the number of divisors of $7\times 11^2=6$
and the number of divisors of $2\times 61=4$
$\Rightarrow 8,6,4$ are in AP with common difference $-2$.